I'm a fan of covers too. Often, when I have a song that I really like, I tend to seek out cover versions to see how other artists interpret the song. For example, I have a number of versions of the song "Gentle On My Mind." In addition to Glen Campbell's hit version I also have versions by John Hartford (the song's writer), Leonard Nimoy (purchased out of curiosity), and Roger Miller (my favorite version).
Sometimes, a song is recorded by many artists before being a hit. An example of this is the song "Close To You." While the Carpenters had a hit with the song, per Wikipedia, the song was previously recorded by both Richard Chamberlain and Dionne Warwick, and the song has been covered by other many other artists since the Carpenters had their hit version.
Something else I've discovered when seeking out covers is that some songs undergo significant changes on they way to being a hit. An example is the song "Trying To Get The Feeling Again." While the song was a hit for Barry Manilow, per the SongFacts website (http://www.songfacts.com/detail.php?id=6816
) it was originally written for the Carpenters (their version was released in 1995). The Manilow version contains lyrics, such as the song's opening lines, that are signficantly different from the Carpenters version.